4710c53dca
These files are a subset of the python-2.7.2.tgz distribution from python.org. Changed files from PyMod-2.7.2 have been copied into the corresponding directories of this tree, replacing the original files in the distribution. Signed-off-by: daryl.mcdaniel@intel.com git-svn-id: https://edk2.svn.sourceforge.net/svnroot/edk2/trunk/edk2@13197 6f19259b-4bc3-4df7-8a09-765794883524
1907 lines
51 KiB
Python
1907 lines
51 KiB
Python
tutorial_tests = """
|
|
Let's try a simple generator:
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... yield 2
|
|
|
|
>>> for i in f():
|
|
... print i
|
|
1
|
|
2
|
|
>>> g = f()
|
|
>>> g.next()
|
|
1
|
|
>>> g.next()
|
|
2
|
|
|
|
"Falling off the end" stops the generator:
|
|
|
|
>>> g.next()
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
File "<stdin>", line 2, in g
|
|
StopIteration
|
|
|
|
"return" also stops the generator:
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... return
|
|
... yield 2 # never reached
|
|
...
|
|
>>> g = f()
|
|
>>> g.next()
|
|
1
|
|
>>> g.next()
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
File "<stdin>", line 3, in f
|
|
StopIteration
|
|
>>> g.next() # once stopped, can't be resumed
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
StopIteration
|
|
|
|
"raise StopIteration" stops the generator too:
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... raise StopIteration
|
|
... yield 2 # never reached
|
|
...
|
|
>>> g = f()
|
|
>>> g.next()
|
|
1
|
|
>>> g.next()
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
StopIteration
|
|
>>> g.next()
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
StopIteration
|
|
|
|
However, they are not exactly equivalent:
|
|
|
|
>>> def g1():
|
|
... try:
|
|
... return
|
|
... except:
|
|
... yield 1
|
|
...
|
|
>>> list(g1())
|
|
[]
|
|
|
|
>>> def g2():
|
|
... try:
|
|
... raise StopIteration
|
|
... except:
|
|
... yield 42
|
|
>>> print list(g2())
|
|
[42]
|
|
|
|
This may be surprising at first:
|
|
|
|
>>> def g3():
|
|
... try:
|
|
... return
|
|
... finally:
|
|
... yield 1
|
|
...
|
|
>>> list(g3())
|
|
[1]
|
|
|
|
Let's create an alternate range() function implemented as a generator:
|
|
|
|
>>> def yrange(n):
|
|
... for i in range(n):
|
|
... yield i
|
|
...
|
|
>>> list(yrange(5))
|
|
[0, 1, 2, 3, 4]
|
|
|
|
Generators always return to the most recent caller:
|
|
|
|
>>> def creator():
|
|
... r = yrange(5)
|
|
... print "creator", r.next()
|
|
... return r
|
|
...
|
|
>>> def caller():
|
|
... r = creator()
|
|
... for i in r:
|
|
... print "caller", i
|
|
...
|
|
>>> caller()
|
|
creator 0
|
|
caller 1
|
|
caller 2
|
|
caller 3
|
|
caller 4
|
|
|
|
Generators can call other generators:
|
|
|
|
>>> def zrange(n):
|
|
... for i in yrange(n):
|
|
... yield i
|
|
...
|
|
>>> list(zrange(5))
|
|
[0, 1, 2, 3, 4]
|
|
|
|
"""
|
|
|
|
# The examples from PEP 255.
|
|
|
|
pep_tests = """
|
|
|
|
Specification: Yield
|
|
|
|
Restriction: A generator cannot be resumed while it is actively
|
|
running:
|
|
|
|
>>> def g():
|
|
... i = me.next()
|
|
... yield i
|
|
>>> me = g()
|
|
>>> me.next()
|
|
Traceback (most recent call last):
|
|
...
|
|
File "<string>", line 2, in g
|
|
ValueError: generator already executing
|
|
|
|
Specification: Return
|
|
|
|
Note that return isn't always equivalent to raising StopIteration: the
|
|
difference lies in how enclosing try/except constructs are treated.
|
|
For example,
|
|
|
|
>>> def f1():
|
|
... try:
|
|
... return
|
|
... except:
|
|
... yield 1
|
|
>>> print list(f1())
|
|
[]
|
|
|
|
because, as in any function, return simply exits, but
|
|
|
|
>>> def f2():
|
|
... try:
|
|
... raise StopIteration
|
|
... except:
|
|
... yield 42
|
|
>>> print list(f2())
|
|
[42]
|
|
|
|
because StopIteration is captured by a bare "except", as is any
|
|
exception.
|
|
|
|
Specification: Generators and Exception Propagation
|
|
|
|
>>> def f():
|
|
... return 1//0
|
|
>>> def g():
|
|
... yield f() # the zero division exception propagates
|
|
... yield 42 # and we'll never get here
|
|
>>> k = g()
|
|
>>> k.next()
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
File "<stdin>", line 2, in g
|
|
File "<stdin>", line 2, in f
|
|
ZeroDivisionError: integer division or modulo by zero
|
|
>>> k.next() # and the generator cannot be resumed
|
|
Traceback (most recent call last):
|
|
File "<stdin>", line 1, in ?
|
|
StopIteration
|
|
>>>
|
|
|
|
Specification: Try/Except/Finally
|
|
|
|
>>> def f():
|
|
... try:
|
|
... yield 1
|
|
... try:
|
|
... yield 2
|
|
... 1//0
|
|
... yield 3 # never get here
|
|
... except ZeroDivisionError:
|
|
... yield 4
|
|
... yield 5
|
|
... raise
|
|
... except:
|
|
... yield 6
|
|
... yield 7 # the "raise" above stops this
|
|
... except:
|
|
... yield 8
|
|
... yield 9
|
|
... try:
|
|
... x = 12
|
|
... finally:
|
|
... yield 10
|
|
... yield 11
|
|
>>> print list(f())
|
|
[1, 2, 4, 5, 8, 9, 10, 11]
|
|
>>>
|
|
|
|
Guido's binary tree example.
|
|
|
|
>>> # A binary tree class.
|
|
>>> class Tree:
|
|
...
|
|
... def __init__(self, label, left=None, right=None):
|
|
... self.label = label
|
|
... self.left = left
|
|
... self.right = right
|
|
...
|
|
... def __repr__(self, level=0, indent=" "):
|
|
... s = level*indent + repr(self.label)
|
|
... if self.left:
|
|
... s = s + "\\n" + self.left.__repr__(level+1, indent)
|
|
... if self.right:
|
|
... s = s + "\\n" + self.right.__repr__(level+1, indent)
|
|
... return s
|
|
...
|
|
... def __iter__(self):
|
|
... return inorder(self)
|
|
|
|
>>> # Create a Tree from a list.
|
|
>>> def tree(list):
|
|
... n = len(list)
|
|
... if n == 0:
|
|
... return []
|
|
... i = n // 2
|
|
... return Tree(list[i], tree(list[:i]), tree(list[i+1:]))
|
|
|
|
>>> # Show it off: create a tree.
|
|
>>> t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
|
|
|
|
>>> # A recursive generator that generates Tree labels in in-order.
|
|
>>> def inorder(t):
|
|
... if t:
|
|
... for x in inorder(t.left):
|
|
... yield x
|
|
... yield t.label
|
|
... for x in inorder(t.right):
|
|
... yield x
|
|
|
|
>>> # Show it off: create a tree.
|
|
>>> t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
|
|
>>> # Print the nodes of the tree in in-order.
|
|
>>> for x in t:
|
|
... print x,
|
|
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
|
|
|
|
>>> # A non-recursive generator.
|
|
>>> def inorder(node):
|
|
... stack = []
|
|
... while node:
|
|
... while node.left:
|
|
... stack.append(node)
|
|
... node = node.left
|
|
... yield node.label
|
|
... while not node.right:
|
|
... try:
|
|
... node = stack.pop()
|
|
... except IndexError:
|
|
... return
|
|
... yield node.label
|
|
... node = node.right
|
|
|
|
>>> # Exercise the non-recursive generator.
|
|
>>> for x in t:
|
|
... print x,
|
|
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
|
|
|
|
"""
|
|
|
|
# Examples from Iterator-List and Python-Dev and c.l.py.
|
|
|
|
email_tests = """
|
|
|
|
The difference between yielding None and returning it.
|
|
|
|
>>> def g():
|
|
... for i in range(3):
|
|
... yield None
|
|
... yield None
|
|
... return
|
|
>>> list(g())
|
|
[None, None, None, None]
|
|
|
|
Ensure that explicitly raising StopIteration acts like any other exception
|
|
in try/except, not like a return.
|
|
|
|
>>> def g():
|
|
... yield 1
|
|
... try:
|
|
... raise StopIteration
|
|
... except:
|
|
... yield 2
|
|
... yield 3
|
|
>>> list(g())
|
|
[1, 2, 3]
|
|
|
|
Next one was posted to c.l.py.
|
|
|
|
>>> def gcomb(x, k):
|
|
... "Generate all combinations of k elements from list x."
|
|
...
|
|
... if k > len(x):
|
|
... return
|
|
... if k == 0:
|
|
... yield []
|
|
... else:
|
|
... first, rest = x[0], x[1:]
|
|
... # A combination does or doesn't contain first.
|
|
... # If it does, the remainder is a k-1 comb of rest.
|
|
... for c in gcomb(rest, k-1):
|
|
... c.insert(0, first)
|
|
... yield c
|
|
... # If it doesn't contain first, it's a k comb of rest.
|
|
... for c in gcomb(rest, k):
|
|
... yield c
|
|
|
|
>>> seq = range(1, 5)
|
|
>>> for k in range(len(seq) + 2):
|
|
... print "%d-combs of %s:" % (k, seq)
|
|
... for c in gcomb(seq, k):
|
|
... print " ", c
|
|
0-combs of [1, 2, 3, 4]:
|
|
[]
|
|
1-combs of [1, 2, 3, 4]:
|
|
[1]
|
|
[2]
|
|
[3]
|
|
[4]
|
|
2-combs of [1, 2, 3, 4]:
|
|
[1, 2]
|
|
[1, 3]
|
|
[1, 4]
|
|
[2, 3]
|
|
[2, 4]
|
|
[3, 4]
|
|
3-combs of [1, 2, 3, 4]:
|
|
[1, 2, 3]
|
|
[1, 2, 4]
|
|
[1, 3, 4]
|
|
[2, 3, 4]
|
|
4-combs of [1, 2, 3, 4]:
|
|
[1, 2, 3, 4]
|
|
5-combs of [1, 2, 3, 4]:
|
|
|
|
From the Iterators list, about the types of these things.
|
|
|
|
>>> def g():
|
|
... yield 1
|
|
...
|
|
>>> type(g)
|
|
<type 'function'>
|
|
>>> i = g()
|
|
>>> type(i)
|
|
<type 'generator'>
|
|
>>> [s for s in dir(i) if not s.startswith('_')]
|
|
['close', 'gi_code', 'gi_frame', 'gi_running', 'next', 'send', 'throw']
|
|
>>> print i.next.__doc__
|
|
x.next() -> the next value, or raise StopIteration
|
|
>>> iter(i) is i
|
|
True
|
|
>>> import types
|
|
>>> isinstance(i, types.GeneratorType)
|
|
True
|
|
|
|
And more, added later.
|
|
|
|
>>> i.gi_running
|
|
0
|
|
>>> type(i.gi_frame)
|
|
<type 'frame'>
|
|
>>> i.gi_running = 42
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: readonly attribute
|
|
>>> def g():
|
|
... yield me.gi_running
|
|
>>> me = g()
|
|
>>> me.gi_running
|
|
0
|
|
>>> me.next()
|
|
1
|
|
>>> me.gi_running
|
|
0
|
|
|
|
A clever union-find implementation from c.l.py, due to David Eppstein.
|
|
Sent: Friday, June 29, 2001 12:16 PM
|
|
To: python-list@python.org
|
|
Subject: Re: PEP 255: Simple Generators
|
|
|
|
>>> class disjointSet:
|
|
... def __init__(self, name):
|
|
... self.name = name
|
|
... self.parent = None
|
|
... self.generator = self.generate()
|
|
...
|
|
... def generate(self):
|
|
... while not self.parent:
|
|
... yield self
|
|
... for x in self.parent.generator:
|
|
... yield x
|
|
...
|
|
... def find(self):
|
|
... return self.generator.next()
|
|
...
|
|
... def union(self, parent):
|
|
... if self.parent:
|
|
... raise ValueError("Sorry, I'm not a root!")
|
|
... self.parent = parent
|
|
...
|
|
... def __str__(self):
|
|
... return self.name
|
|
|
|
>>> names = "ABCDEFGHIJKLM"
|
|
>>> sets = [disjointSet(name) for name in names]
|
|
>>> roots = sets[:]
|
|
|
|
>>> import random
|
|
>>> gen = random.WichmannHill(42)
|
|
>>> while 1:
|
|
... for s in sets:
|
|
... print "%s->%s" % (s, s.find()),
|
|
... print
|
|
... if len(roots) > 1:
|
|
... s1 = gen.choice(roots)
|
|
... roots.remove(s1)
|
|
... s2 = gen.choice(roots)
|
|
... s1.union(s2)
|
|
... print "merged", s1, "into", s2
|
|
... else:
|
|
... break
|
|
A->A B->B C->C D->D E->E F->F G->G H->H I->I J->J K->K L->L M->M
|
|
merged D into G
|
|
A->A B->B C->C D->G E->E F->F G->G H->H I->I J->J K->K L->L M->M
|
|
merged C into F
|
|
A->A B->B C->F D->G E->E F->F G->G H->H I->I J->J K->K L->L M->M
|
|
merged L into A
|
|
A->A B->B C->F D->G E->E F->F G->G H->H I->I J->J K->K L->A M->M
|
|
merged H into E
|
|
A->A B->B C->F D->G E->E F->F G->G H->E I->I J->J K->K L->A M->M
|
|
merged B into E
|
|
A->A B->E C->F D->G E->E F->F G->G H->E I->I J->J K->K L->A M->M
|
|
merged J into G
|
|
A->A B->E C->F D->G E->E F->F G->G H->E I->I J->G K->K L->A M->M
|
|
merged E into G
|
|
A->A B->G C->F D->G E->G F->F G->G H->G I->I J->G K->K L->A M->M
|
|
merged M into G
|
|
A->A B->G C->F D->G E->G F->F G->G H->G I->I J->G K->K L->A M->G
|
|
merged I into K
|
|
A->A B->G C->F D->G E->G F->F G->G H->G I->K J->G K->K L->A M->G
|
|
merged K into A
|
|
A->A B->G C->F D->G E->G F->F G->G H->G I->A J->G K->A L->A M->G
|
|
merged F into A
|
|
A->A B->G C->A D->G E->G F->A G->G H->G I->A J->G K->A L->A M->G
|
|
merged A into G
|
|
A->G B->G C->G D->G E->G F->G G->G H->G I->G J->G K->G L->G M->G
|
|
|
|
"""
|
|
# Emacs turd '
|
|
|
|
# Fun tests (for sufficiently warped notions of "fun").
|
|
|
|
fun_tests = """
|
|
|
|
Build up to a recursive Sieve of Eratosthenes generator.
|
|
|
|
>>> def firstn(g, n):
|
|
... return [g.next() for i in range(n)]
|
|
|
|
>>> def intsfrom(i):
|
|
... while 1:
|
|
... yield i
|
|
... i += 1
|
|
|
|
>>> firstn(intsfrom(5), 7)
|
|
[5, 6, 7, 8, 9, 10, 11]
|
|
|
|
>>> def exclude_multiples(n, ints):
|
|
... for i in ints:
|
|
... if i % n:
|
|
... yield i
|
|
|
|
>>> firstn(exclude_multiples(3, intsfrom(1)), 6)
|
|
[1, 2, 4, 5, 7, 8]
|
|
|
|
>>> def sieve(ints):
|
|
... prime = ints.next()
|
|
... yield prime
|
|
... not_divisible_by_prime = exclude_multiples(prime, ints)
|
|
... for p in sieve(not_divisible_by_prime):
|
|
... yield p
|
|
|
|
>>> primes = sieve(intsfrom(2))
|
|
>>> firstn(primes, 20)
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
|
|
|
|
|
|
Another famous problem: generate all integers of the form
|
|
2**i * 3**j * 5**k
|
|
in increasing order, where i,j,k >= 0. Trickier than it may look at first!
|
|
Try writing it without generators, and correctly, and without generating
|
|
3 internal results for each result output.
|
|
|
|
>>> def times(n, g):
|
|
... for i in g:
|
|
... yield n * i
|
|
>>> firstn(times(10, intsfrom(1)), 10)
|
|
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
|
|
|
|
>>> def merge(g, h):
|
|
... ng = g.next()
|
|
... nh = h.next()
|
|
... while 1:
|
|
... if ng < nh:
|
|
... yield ng
|
|
... ng = g.next()
|
|
... elif ng > nh:
|
|
... yield nh
|
|
... nh = h.next()
|
|
... else:
|
|
... yield ng
|
|
... ng = g.next()
|
|
... nh = h.next()
|
|
|
|
The following works, but is doing a whale of a lot of redundant work --
|
|
it's not clear how to get the internal uses of m235 to share a single
|
|
generator. Note that me_times2 (etc) each need to see every element in the
|
|
result sequence. So this is an example where lazy lists are more natural
|
|
(you can look at the head of a lazy list any number of times).
|
|
|
|
>>> def m235():
|
|
... yield 1
|
|
... me_times2 = times(2, m235())
|
|
... me_times3 = times(3, m235())
|
|
... me_times5 = times(5, m235())
|
|
... for i in merge(merge(me_times2,
|
|
... me_times3),
|
|
... me_times5):
|
|
... yield i
|
|
|
|
Don't print "too many" of these -- the implementation above is extremely
|
|
inefficient: each call of m235() leads to 3 recursive calls, and in
|
|
turn each of those 3 more, and so on, and so on, until we've descended
|
|
enough levels to satisfy the print stmts. Very odd: when I printed 5
|
|
lines of results below, this managed to screw up Win98's malloc in "the
|
|
usual" way, i.e. the heap grew over 4Mb so Win98 started fragmenting
|
|
address space, and it *looked* like a very slow leak.
|
|
|
|
>>> result = m235()
|
|
>>> for i in range(3):
|
|
... print firstn(result, 15)
|
|
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
|
|
[25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
|
|
[81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
|
|
|
|
Heh. Here's one way to get a shared list, complete with an excruciating
|
|
namespace renaming trick. The *pretty* part is that the times() and merge()
|
|
functions can be reused as-is, because they only assume their stream
|
|
arguments are iterable -- a LazyList is the same as a generator to times().
|
|
|
|
>>> class LazyList:
|
|
... def __init__(self, g):
|
|
... self.sofar = []
|
|
... self.fetch = g.next
|
|
...
|
|
... def __getitem__(self, i):
|
|
... sofar, fetch = self.sofar, self.fetch
|
|
... while i >= len(sofar):
|
|
... sofar.append(fetch())
|
|
... return sofar[i]
|
|
|
|
>>> def m235():
|
|
... yield 1
|
|
... # Gack: m235 below actually refers to a LazyList.
|
|
... me_times2 = times(2, m235)
|
|
... me_times3 = times(3, m235)
|
|
... me_times5 = times(5, m235)
|
|
... for i in merge(merge(me_times2,
|
|
... me_times3),
|
|
... me_times5):
|
|
... yield i
|
|
|
|
Print as many of these as you like -- *this* implementation is memory-
|
|
efficient.
|
|
|
|
>>> m235 = LazyList(m235())
|
|
>>> for i in range(5):
|
|
... print [m235[j] for j in range(15*i, 15*(i+1))]
|
|
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
|
|
[25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
|
|
[81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
|
|
[200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384]
|
|
[400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675]
|
|
|
|
Ye olde Fibonacci generator, LazyList style.
|
|
|
|
>>> def fibgen(a, b):
|
|
...
|
|
... def sum(g, h):
|
|
... while 1:
|
|
... yield g.next() + h.next()
|
|
...
|
|
... def tail(g):
|
|
... g.next() # throw first away
|
|
... for x in g:
|
|
... yield x
|
|
...
|
|
... yield a
|
|
... yield b
|
|
... for s in sum(iter(fib),
|
|
... tail(iter(fib))):
|
|
... yield s
|
|
|
|
>>> fib = LazyList(fibgen(1, 2))
|
|
>>> firstn(iter(fib), 17)
|
|
[1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
|
|
|
|
|
|
Running after your tail with itertools.tee (new in version 2.4)
|
|
|
|
The algorithms "m235" (Hamming) and Fibonacci presented above are both
|
|
examples of a whole family of FP (functional programming) algorithms
|
|
where a function produces and returns a list while the production algorithm
|
|
suppose the list as already produced by recursively calling itself.
|
|
For these algorithms to work, they must:
|
|
|
|
- produce at least a first element without presupposing the existence of
|
|
the rest of the list
|
|
- produce their elements in a lazy manner
|
|
|
|
To work efficiently, the beginning of the list must not be recomputed over
|
|
and over again. This is ensured in most FP languages as a built-in feature.
|
|
In python, we have to explicitly maintain a list of already computed results
|
|
and abandon genuine recursivity.
|
|
|
|
This is what had been attempted above with the LazyList class. One problem
|
|
with that class is that it keeps a list of all of the generated results and
|
|
therefore continually grows. This partially defeats the goal of the generator
|
|
concept, viz. produce the results only as needed instead of producing them
|
|
all and thereby wasting memory.
|
|
|
|
Thanks to itertools.tee, it is now clear "how to get the internal uses of
|
|
m235 to share a single generator".
|
|
|
|
>>> from itertools import tee
|
|
>>> def m235():
|
|
... def _m235():
|
|
... yield 1
|
|
... for n in merge(times(2, m2),
|
|
... merge(times(3, m3),
|
|
... times(5, m5))):
|
|
... yield n
|
|
... m1 = _m235()
|
|
... m2, m3, m5, mRes = tee(m1, 4)
|
|
... return mRes
|
|
|
|
>>> it = m235()
|
|
>>> for i in range(5):
|
|
... print firstn(it, 15)
|
|
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
|
|
[25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
|
|
[81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
|
|
[200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384]
|
|
[400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675]
|
|
|
|
The "tee" function does just what we want. It internally keeps a generated
|
|
result for as long as it has not been "consumed" from all of the duplicated
|
|
iterators, whereupon it is deleted. You can therefore print the hamming
|
|
sequence during hours without increasing memory usage, or very little.
|
|
|
|
The beauty of it is that recursive running-after-their-tail FP algorithms
|
|
are quite straightforwardly expressed with this Python idiom.
|
|
|
|
Ye olde Fibonacci generator, tee style.
|
|
|
|
>>> def fib():
|
|
...
|
|
... def _isum(g, h):
|
|
... while 1:
|
|
... yield g.next() + h.next()
|
|
...
|
|
... def _fib():
|
|
... yield 1
|
|
... yield 2
|
|
... fibTail.next() # throw first away
|
|
... for res in _isum(fibHead, fibTail):
|
|
... yield res
|
|
...
|
|
... realfib = _fib()
|
|
... fibHead, fibTail, fibRes = tee(realfib, 3)
|
|
... return fibRes
|
|
|
|
>>> firstn(fib(), 17)
|
|
[1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
|
|
|
|
"""
|
|
|
|
# syntax_tests mostly provokes SyntaxErrors. Also fiddling with #if 0
|
|
# hackery.
|
|
|
|
syntax_tests = """
|
|
|
|
>>> def f():
|
|
... return 22
|
|
... yield 1
|
|
Traceback (most recent call last):
|
|
..
|
|
SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[0]>, line 3)
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... return 22
|
|
Traceback (most recent call last):
|
|
..
|
|
SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[1]>, line 3)
|
|
|
|
"return None" is not the same as "return" in a generator:
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... return None
|
|
Traceback (most recent call last):
|
|
..
|
|
SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[2]>, line 3)
|
|
|
|
These are fine:
|
|
|
|
>>> def f():
|
|
... yield 1
|
|
... return
|
|
|
|
>>> def f():
|
|
... try:
|
|
... yield 1
|
|
... finally:
|
|
... pass
|
|
|
|
>>> def f():
|
|
... try:
|
|
... try:
|
|
... 1//0
|
|
... except ZeroDivisionError:
|
|
... yield 666
|
|
... except:
|
|
... pass
|
|
... finally:
|
|
... pass
|
|
|
|
>>> def f():
|
|
... try:
|
|
... try:
|
|
... yield 12
|
|
... 1//0
|
|
... except ZeroDivisionError:
|
|
... yield 666
|
|
... except:
|
|
... try:
|
|
... x = 12
|
|
... finally:
|
|
... yield 12
|
|
... except:
|
|
... return
|
|
>>> list(f())
|
|
[12, 666]
|
|
|
|
>>> def f():
|
|
... yield
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... yield
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... yield 1
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f():
|
|
... if "":
|
|
... yield None
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f():
|
|
... return
|
|
... try:
|
|
... if x==4:
|
|
... pass
|
|
... elif 0:
|
|
... try:
|
|
... 1//0
|
|
... except SyntaxError:
|
|
... pass
|
|
... else:
|
|
... if 0:
|
|
... while 12:
|
|
... x += 1
|
|
... yield 2 # don't blink
|
|
... f(a, b, c, d, e)
|
|
... else:
|
|
... pass
|
|
... except:
|
|
... x = 1
|
|
... return
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... def g():
|
|
... yield 1
|
|
...
|
|
>>> type(f())
|
|
<type 'NoneType'>
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... class C:
|
|
... def __init__(self):
|
|
... yield 1
|
|
... def f(self):
|
|
... yield 2
|
|
>>> type(f())
|
|
<type 'NoneType'>
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... return
|
|
... if 0:
|
|
... yield 2
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
|
|
>>> def f():
|
|
... if 0:
|
|
... lambda x: x # shouldn't trigger here
|
|
... return # or here
|
|
... def f(i):
|
|
... return 2*i # or here
|
|
... if 0:
|
|
... return 3 # but *this* sucks (line 8)
|
|
... if 0:
|
|
... yield 2 # because it's a generator (line 10)
|
|
Traceback (most recent call last):
|
|
SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[24]>, line 10)
|
|
|
|
This one caused a crash (see SF bug 567538):
|
|
|
|
>>> def f():
|
|
... for i in range(3):
|
|
... try:
|
|
... continue
|
|
... finally:
|
|
... yield i
|
|
...
|
|
>>> g = f()
|
|
>>> print g.next()
|
|
0
|
|
>>> print g.next()
|
|
1
|
|
>>> print g.next()
|
|
2
|
|
>>> print g.next()
|
|
Traceback (most recent call last):
|
|
StopIteration
|
|
|
|
|
|
Test the gi_code attribute
|
|
|
|
>>> def f():
|
|
... yield 5
|
|
...
|
|
>>> g = f()
|
|
>>> g.gi_code is f.func_code
|
|
True
|
|
>>> g.next()
|
|
5
|
|
>>> g.next()
|
|
Traceback (most recent call last):
|
|
StopIteration
|
|
>>> g.gi_code is f.func_code
|
|
True
|
|
|
|
|
|
Test the __name__ attribute and the repr()
|
|
|
|
>>> def f():
|
|
... yield 5
|
|
...
|
|
>>> g = f()
|
|
>>> g.__name__
|
|
'f'
|
|
>>> repr(g) # doctest: +ELLIPSIS
|
|
'<generator object f at ...>'
|
|
|
|
Lambdas shouldn't have their usual return behavior.
|
|
|
|
>>> x = lambda: (yield 1)
|
|
>>> list(x())
|
|
[1]
|
|
|
|
>>> x = lambda: ((yield 1), (yield 2))
|
|
>>> list(x())
|
|
[1, 2]
|
|
"""
|
|
|
|
# conjoin is a simple backtracking generator, named in honor of Icon's
|
|
# "conjunction" control structure. Pass a list of no-argument functions
|
|
# that return iterable objects. Easiest to explain by example: assume the
|
|
# function list [x, y, z] is passed. Then conjoin acts like:
|
|
#
|
|
# def g():
|
|
# values = [None] * 3
|
|
# for values[0] in x():
|
|
# for values[1] in y():
|
|
# for values[2] in z():
|
|
# yield values
|
|
#
|
|
# So some 3-lists of values *may* be generated, each time we successfully
|
|
# get into the innermost loop. If an iterator fails (is exhausted) before
|
|
# then, it "backtracks" to get the next value from the nearest enclosing
|
|
# iterator (the one "to the left"), and starts all over again at the next
|
|
# slot (pumps a fresh iterator). Of course this is most useful when the
|
|
# iterators have side-effects, so that which values *can* be generated at
|
|
# each slot depend on the values iterated at previous slots.
|
|
|
|
def simple_conjoin(gs):
|
|
|
|
values = [None] * len(gs)
|
|
|
|
def gen(i):
|
|
if i >= len(gs):
|
|
yield values
|
|
else:
|
|
for values[i] in gs[i]():
|
|
for x in gen(i+1):
|
|
yield x
|
|
|
|
for x in gen(0):
|
|
yield x
|
|
|
|
# That works fine, but recursing a level and checking i against len(gs) for
|
|
# each item produced is inefficient. By doing manual loop unrolling across
|
|
# generator boundaries, it's possible to eliminate most of that overhead.
|
|
# This isn't worth the bother *in general* for generators, but conjoin() is
|
|
# a core building block for some CPU-intensive generator applications.
|
|
|
|
def conjoin(gs):
|
|
|
|
n = len(gs)
|
|
values = [None] * n
|
|
|
|
# Do one loop nest at time recursively, until the # of loop nests
|
|
# remaining is divisible by 3.
|
|
|
|
def gen(i):
|
|
if i >= n:
|
|
yield values
|
|
|
|
elif (n-i) % 3:
|
|
ip1 = i+1
|
|
for values[i] in gs[i]():
|
|
for x in gen(ip1):
|
|
yield x
|
|
|
|
else:
|
|
for x in _gen3(i):
|
|
yield x
|
|
|
|
# Do three loop nests at a time, recursing only if at least three more
|
|
# remain. Don't call directly: this is an internal optimization for
|
|
# gen's use.
|
|
|
|
def _gen3(i):
|
|
assert i < n and (n-i) % 3 == 0
|
|
ip1, ip2, ip3 = i+1, i+2, i+3
|
|
g, g1, g2 = gs[i : ip3]
|
|
|
|
if ip3 >= n:
|
|
# These are the last three, so we can yield values directly.
|
|
for values[i] in g():
|
|
for values[ip1] in g1():
|
|
for values[ip2] in g2():
|
|
yield values
|
|
|
|
else:
|
|
# At least 6 loop nests remain; peel off 3 and recurse for the
|
|
# rest.
|
|
for values[i] in g():
|
|
for values[ip1] in g1():
|
|
for values[ip2] in g2():
|
|
for x in _gen3(ip3):
|
|
yield x
|
|
|
|
for x in gen(0):
|
|
yield x
|
|
|
|
# And one more approach: For backtracking apps like the Knight's Tour
|
|
# solver below, the number of backtracking levels can be enormous (one
|
|
# level per square, for the Knight's Tour, so that e.g. a 100x100 board
|
|
# needs 10,000 levels). In such cases Python is likely to run out of
|
|
# stack space due to recursion. So here's a recursion-free version of
|
|
# conjoin too.
|
|
# NOTE WELL: This allows large problems to be solved with only trivial
|
|
# demands on stack space. Without explicitly resumable generators, this is
|
|
# much harder to achieve. OTOH, this is much slower (up to a factor of 2)
|
|
# than the fancy unrolled recursive conjoin.
|
|
|
|
def flat_conjoin(gs): # rename to conjoin to run tests with this instead
|
|
n = len(gs)
|
|
values = [None] * n
|
|
iters = [None] * n
|
|
_StopIteration = StopIteration # make local because caught a *lot*
|
|
i = 0
|
|
while 1:
|
|
# Descend.
|
|
try:
|
|
while i < n:
|
|
it = iters[i] = gs[i]().next
|
|
values[i] = it()
|
|
i += 1
|
|
except _StopIteration:
|
|
pass
|
|
else:
|
|
assert i == n
|
|
yield values
|
|
|
|
# Backtrack until an older iterator can be resumed.
|
|
i -= 1
|
|
while i >= 0:
|
|
try:
|
|
values[i] = iters[i]()
|
|
# Success! Start fresh at next level.
|
|
i += 1
|
|
break
|
|
except _StopIteration:
|
|
# Continue backtracking.
|
|
i -= 1
|
|
else:
|
|
assert i < 0
|
|
break
|
|
|
|
# A conjoin-based N-Queens solver.
|
|
|
|
class Queens:
|
|
def __init__(self, n):
|
|
self.n = n
|
|
rangen = range(n)
|
|
|
|
# Assign a unique int to each column and diagonal.
|
|
# columns: n of those, range(n).
|
|
# NW-SE diagonals: 2n-1 of these, i-j unique and invariant along
|
|
# each, smallest i-j is 0-(n-1) = 1-n, so add n-1 to shift to 0-
|
|
# based.
|
|
# NE-SW diagonals: 2n-1 of these, i+j unique and invariant along
|
|
# each, smallest i+j is 0, largest is 2n-2.
|
|
|
|
# For each square, compute a bit vector of the columns and
|
|
# diagonals it covers, and for each row compute a function that
|
|
# generates the possiblities for the columns in that row.
|
|
self.rowgenerators = []
|
|
for i in rangen:
|
|
rowuses = [(1L << j) | # column ordinal
|
|
(1L << (n + i-j + n-1)) | # NW-SE ordinal
|
|
(1L << (n + 2*n-1 + i+j)) # NE-SW ordinal
|
|
for j in rangen]
|
|
|
|
def rowgen(rowuses=rowuses):
|
|
for j in rangen:
|
|
uses = rowuses[j]
|
|
if uses & self.used == 0:
|
|
self.used |= uses
|
|
yield j
|
|
self.used &= ~uses
|
|
|
|
self.rowgenerators.append(rowgen)
|
|
|
|
# Generate solutions.
|
|
def solve(self):
|
|
self.used = 0
|
|
for row2col in conjoin(self.rowgenerators):
|
|
yield row2col
|
|
|
|
def printsolution(self, row2col):
|
|
n = self.n
|
|
assert n == len(row2col)
|
|
sep = "+" + "-+" * n
|
|
print sep
|
|
for i in range(n):
|
|
squares = [" " for j in range(n)]
|
|
squares[row2col[i]] = "Q"
|
|
print "|" + "|".join(squares) + "|"
|
|
print sep
|
|
|
|
# A conjoin-based Knight's Tour solver. This is pretty sophisticated
|
|
# (e.g., when used with flat_conjoin above, and passing hard=1 to the
|
|
# constructor, a 200x200 Knight's Tour was found quickly -- note that we're
|
|
# creating 10s of thousands of generators then!), and is lengthy.
|
|
|
|
class Knights:
|
|
def __init__(self, m, n, hard=0):
|
|
self.m, self.n = m, n
|
|
|
|
# solve() will set up succs[i] to be a list of square #i's
|
|
# successors.
|
|
succs = self.succs = []
|
|
|
|
# Remove i0 from each of its successor's successor lists, i.e.
|
|
# successors can't go back to i0 again. Return 0 if we can
|
|
# detect this makes a solution impossible, else return 1.
|
|
|
|
def remove_from_successors(i0, len=len):
|
|
# If we remove all exits from a free square, we're dead:
|
|
# even if we move to it next, we can't leave it again.
|
|
# If we create a square with one exit, we must visit it next;
|
|
# else somebody else will have to visit it, and since there's
|
|
# only one adjacent, there won't be a way to leave it again.
|
|
# Finelly, if we create more than one free square with a
|
|
# single exit, we can only move to one of them next, leaving
|
|
# the other one a dead end.
|
|
ne0 = ne1 = 0
|
|
for i in succs[i0]:
|
|
s = succs[i]
|
|
s.remove(i0)
|
|
e = len(s)
|
|
if e == 0:
|
|
ne0 += 1
|
|
elif e == 1:
|
|
ne1 += 1
|
|
return ne0 == 0 and ne1 < 2
|
|
|
|
# Put i0 back in each of its successor's successor lists.
|
|
|
|
def add_to_successors(i0):
|
|
for i in succs[i0]:
|
|
succs[i].append(i0)
|
|
|
|
# Generate the first move.
|
|
def first():
|
|
if m < 1 or n < 1:
|
|
return
|
|
|
|
# Since we're looking for a cycle, it doesn't matter where we
|
|
# start. Starting in a corner makes the 2nd move easy.
|
|
corner = self.coords2index(0, 0)
|
|
remove_from_successors(corner)
|
|
self.lastij = corner
|
|
yield corner
|
|
add_to_successors(corner)
|
|
|
|
# Generate the second moves.
|
|
def second():
|
|
corner = self.coords2index(0, 0)
|
|
assert self.lastij == corner # i.e., we started in the corner
|
|
if m < 3 or n < 3:
|
|
return
|
|
assert len(succs[corner]) == 2
|
|
assert self.coords2index(1, 2) in succs[corner]
|
|
assert self.coords2index(2, 1) in succs[corner]
|
|
# Only two choices. Whichever we pick, the other must be the
|
|
# square picked on move m*n, as it's the only way to get back
|
|
# to (0, 0). Save its index in self.final so that moves before
|
|
# the last know it must be kept free.
|
|
for i, j in (1, 2), (2, 1):
|
|
this = self.coords2index(i, j)
|
|
final = self.coords2index(3-i, 3-j)
|
|
self.final = final
|
|
|
|
remove_from_successors(this)
|
|
succs[final].append(corner)
|
|
self.lastij = this
|
|
yield this
|
|
succs[final].remove(corner)
|
|
add_to_successors(this)
|
|
|
|
# Generate moves 3 thru m*n-1.
|
|
def advance(len=len):
|
|
# If some successor has only one exit, must take it.
|
|
# Else favor successors with fewer exits.
|
|
candidates = []
|
|
for i in succs[self.lastij]:
|
|
e = len(succs[i])
|
|
assert e > 0, "else remove_from_successors() pruning flawed"
|
|
if e == 1:
|
|
candidates = [(e, i)]
|
|
break
|
|
candidates.append((e, i))
|
|
else:
|
|
candidates.sort()
|
|
|
|
for e, i in candidates:
|
|
if i != self.final:
|
|
if remove_from_successors(i):
|
|
self.lastij = i
|
|
yield i
|
|
add_to_successors(i)
|
|
|
|
# Generate moves 3 thru m*n-1. Alternative version using a
|
|
# stronger (but more expensive) heuristic to order successors.
|
|
# Since the # of backtracking levels is m*n, a poor move early on
|
|
# can take eons to undo. Smallest square board for which this
|
|
# matters a lot is 52x52.
|
|
def advance_hard(vmid=(m-1)/2.0, hmid=(n-1)/2.0, len=len):
|
|
# If some successor has only one exit, must take it.
|
|
# Else favor successors with fewer exits.
|
|
# Break ties via max distance from board centerpoint (favor
|
|
# corners and edges whenever possible).
|
|
candidates = []
|
|
for i in succs[self.lastij]:
|
|
e = len(succs[i])
|
|
assert e > 0, "else remove_from_successors() pruning flawed"
|
|
if e == 1:
|
|
candidates = [(e, 0, i)]
|
|
break
|
|
i1, j1 = self.index2coords(i)
|
|
d = (i1 - vmid)**2 + (j1 - hmid)**2
|
|
candidates.append((e, -d, i))
|
|
else:
|
|
candidates.sort()
|
|
|
|
for e, d, i in candidates:
|
|
if i != self.final:
|
|
if remove_from_successors(i):
|
|
self.lastij = i
|
|
yield i
|
|
add_to_successors(i)
|
|
|
|
# Generate the last move.
|
|
def last():
|
|
assert self.final in succs[self.lastij]
|
|
yield self.final
|
|
|
|
if m*n < 4:
|
|
self.squaregenerators = [first]
|
|
else:
|
|
self.squaregenerators = [first, second] + \
|
|
[hard and advance_hard or advance] * (m*n - 3) + \
|
|
[last]
|
|
|
|
def coords2index(self, i, j):
|
|
assert 0 <= i < self.m
|
|
assert 0 <= j < self.n
|
|
return i * self.n + j
|
|
|
|
def index2coords(self, index):
|
|
assert 0 <= index < self.m * self.n
|
|
return divmod(index, self.n)
|
|
|
|
def _init_board(self):
|
|
succs = self.succs
|
|
del succs[:]
|
|
m, n = self.m, self.n
|
|
c2i = self.coords2index
|
|
|
|
offsets = [( 1, 2), ( 2, 1), ( 2, -1), ( 1, -2),
|
|
(-1, -2), (-2, -1), (-2, 1), (-1, 2)]
|
|
rangen = range(n)
|
|
for i in range(m):
|
|
for j in rangen:
|
|
s = [c2i(i+io, j+jo) for io, jo in offsets
|
|
if 0 <= i+io < m and
|
|
0 <= j+jo < n]
|
|
succs.append(s)
|
|
|
|
# Generate solutions.
|
|
def solve(self):
|
|
self._init_board()
|
|
for x in conjoin(self.squaregenerators):
|
|
yield x
|
|
|
|
def printsolution(self, x):
|
|
m, n = self.m, self.n
|
|
assert len(x) == m*n
|
|
w = len(str(m*n))
|
|
format = "%" + str(w) + "d"
|
|
|
|
squares = [[None] * n for i in range(m)]
|
|
k = 1
|
|
for i in x:
|
|
i1, j1 = self.index2coords(i)
|
|
squares[i1][j1] = format % k
|
|
k += 1
|
|
|
|
sep = "+" + ("-" * w + "+") * n
|
|
print sep
|
|
for i in range(m):
|
|
row = squares[i]
|
|
print "|" + "|".join(row) + "|"
|
|
print sep
|
|
|
|
conjoin_tests = """
|
|
|
|
Generate the 3-bit binary numbers in order. This illustrates dumbest-
|
|
possible use of conjoin, just to generate the full cross-product.
|
|
|
|
>>> for c in conjoin([lambda: iter((0, 1))] * 3):
|
|
... print c
|
|
[0, 0, 0]
|
|
[0, 0, 1]
|
|
[0, 1, 0]
|
|
[0, 1, 1]
|
|
[1, 0, 0]
|
|
[1, 0, 1]
|
|
[1, 1, 0]
|
|
[1, 1, 1]
|
|
|
|
For efficiency in typical backtracking apps, conjoin() yields the same list
|
|
object each time. So if you want to save away a full account of its
|
|
generated sequence, you need to copy its results.
|
|
|
|
>>> def gencopy(iterator):
|
|
... for x in iterator:
|
|
... yield x[:]
|
|
|
|
>>> for n in range(10):
|
|
... all = list(gencopy(conjoin([lambda: iter((0, 1))] * n)))
|
|
... print n, len(all), all[0] == [0] * n, all[-1] == [1] * n
|
|
0 1 True True
|
|
1 2 True True
|
|
2 4 True True
|
|
3 8 True True
|
|
4 16 True True
|
|
5 32 True True
|
|
6 64 True True
|
|
7 128 True True
|
|
8 256 True True
|
|
9 512 True True
|
|
|
|
And run an 8-queens solver.
|
|
|
|
>>> q = Queens(8)
|
|
>>> LIMIT = 2
|
|
>>> count = 0
|
|
>>> for row2col in q.solve():
|
|
... count += 1
|
|
... if count <= LIMIT:
|
|
... print "Solution", count
|
|
... q.printsolution(row2col)
|
|
Solution 1
|
|
+-+-+-+-+-+-+-+-+
|
|
|Q| | | | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | |Q| | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | | | |Q|
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | |Q| | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | |Q| | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | | |Q| |
|
|
+-+-+-+-+-+-+-+-+
|
|
| |Q| | | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | |Q| | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
Solution 2
|
|
+-+-+-+-+-+-+-+-+
|
|
|Q| | | | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | |Q| | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | | | |Q|
|
|
+-+-+-+-+-+-+-+-+
|
|
| | |Q| | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | | | |Q| |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | |Q| | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| |Q| | | | | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
| | | | |Q| | | |
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
>>> print count, "solutions in all."
|
|
92 solutions in all.
|
|
|
|
And run a Knight's Tour on a 10x10 board. Note that there are about
|
|
20,000 solutions even on a 6x6 board, so don't dare run this to exhaustion.
|
|
|
|
>>> k = Knights(10, 10)
|
|
>>> LIMIT = 2
|
|
>>> count = 0
|
|
>>> for x in k.solve():
|
|
... count += 1
|
|
... if count <= LIMIT:
|
|
... print "Solution", count
|
|
... k.printsolution(x)
|
|
... else:
|
|
... break
|
|
Solution 1
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 1| 58| 27| 34| 3| 40| 29| 10| 5| 8|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 26| 35| 2| 57| 28| 33| 4| 7| 30| 11|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 59|100| 73| 36| 41| 56| 39| 32| 9| 6|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 74| 25| 60| 55| 72| 37| 42| 49| 12| 31|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 61| 86| 99| 76| 63| 52| 47| 38| 43| 50|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 24| 75| 62| 85| 54| 71| 64| 51| 48| 13|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 87| 98| 91| 80| 77| 84| 53| 46| 65| 44|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 90| 23| 88| 95| 70| 79| 68| 83| 14| 17|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 97| 92| 21| 78| 81| 94| 19| 16| 45| 66|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 22| 89| 96| 93| 20| 69| 82| 67| 18| 15|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
Solution 2
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 1| 58| 27| 34| 3| 40| 29| 10| 5| 8|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 26| 35| 2| 57| 28| 33| 4| 7| 30| 11|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 59|100| 73| 36| 41| 56| 39| 32| 9| 6|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 74| 25| 60| 55| 72| 37| 42| 49| 12| 31|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 61| 86| 99| 76| 63| 52| 47| 38| 43| 50|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 24| 75| 62| 85| 54| 71| 64| 51| 48| 13|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 87| 98| 89| 80| 77| 84| 53| 46| 65| 44|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 90| 23| 92| 95| 70| 79| 68| 83| 14| 17|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 97| 88| 21| 78| 81| 94| 19| 16| 45| 66|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
| 22| 91| 96| 93| 20| 69| 82| 67| 18| 15|
|
|
+---+---+---+---+---+---+---+---+---+---+
|
|
"""
|
|
|
|
weakref_tests = """\
|
|
Generators are weakly referencable:
|
|
|
|
>>> import weakref
|
|
>>> def gen():
|
|
... yield 'foo!'
|
|
...
|
|
>>> wr = weakref.ref(gen)
|
|
>>> wr() is gen
|
|
True
|
|
>>> p = weakref.proxy(gen)
|
|
|
|
Generator-iterators are weakly referencable as well:
|
|
|
|
>>> gi = gen()
|
|
>>> wr = weakref.ref(gi)
|
|
>>> wr() is gi
|
|
True
|
|
>>> p = weakref.proxy(gi)
|
|
>>> list(p)
|
|
['foo!']
|
|
|
|
"""
|
|
|
|
coroutine_tests = """\
|
|
Sending a value into a started generator:
|
|
|
|
>>> def f():
|
|
... print (yield 1)
|
|
... yield 2
|
|
>>> g = f()
|
|
>>> g.next()
|
|
1
|
|
>>> g.send(42)
|
|
42
|
|
2
|
|
|
|
Sending a value into a new generator produces a TypeError:
|
|
|
|
>>> f().send("foo")
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: can't send non-None value to a just-started generator
|
|
|
|
|
|
Yield by itself yields None:
|
|
|
|
>>> def f(): yield
|
|
>>> list(f())
|
|
[None]
|
|
|
|
|
|
|
|
An obscene abuse of a yield expression within a generator expression:
|
|
|
|
>>> list((yield 21) for i in range(4))
|
|
[21, None, 21, None, 21, None, 21, None]
|
|
|
|
And a more sane, but still weird usage:
|
|
|
|
>>> def f(): list(i for i in [(yield 26)])
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
|
|
A yield expression with augmented assignment.
|
|
|
|
>>> def coroutine(seq):
|
|
... count = 0
|
|
... while count < 200:
|
|
... count += yield
|
|
... seq.append(count)
|
|
>>> seq = []
|
|
>>> c = coroutine(seq)
|
|
>>> c.next()
|
|
>>> print seq
|
|
[]
|
|
>>> c.send(10)
|
|
>>> print seq
|
|
[10]
|
|
>>> c.send(10)
|
|
>>> print seq
|
|
[10, 20]
|
|
>>> c.send(10)
|
|
>>> print seq
|
|
[10, 20, 30]
|
|
|
|
|
|
Check some syntax errors for yield expressions:
|
|
|
|
>>> f=lambda: (yield 1),(yield 2)
|
|
Traceback (most recent call last):
|
|
...
|
|
File "<doctest test.test_generators.__test__.coroutine[21]>", line 1
|
|
SyntaxError: 'yield' outside function
|
|
|
|
>>> def f(): return lambda x=(yield): 1
|
|
Traceback (most recent call last):
|
|
...
|
|
SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.coroutine[22]>, line 1)
|
|
|
|
>>> def f(): x = yield = y
|
|
Traceback (most recent call last):
|
|
...
|
|
File "<doctest test.test_generators.__test__.coroutine[23]>", line 1
|
|
SyntaxError: assignment to yield expression not possible
|
|
|
|
>>> def f(): (yield bar) = y
|
|
Traceback (most recent call last):
|
|
...
|
|
File "<doctest test.test_generators.__test__.coroutine[24]>", line 1
|
|
SyntaxError: can't assign to yield expression
|
|
|
|
>>> def f(): (yield bar) += y
|
|
Traceback (most recent call last):
|
|
...
|
|
File "<doctest test.test_generators.__test__.coroutine[25]>", line 1
|
|
SyntaxError: can't assign to yield expression
|
|
|
|
|
|
Now check some throw() conditions:
|
|
|
|
>>> def f():
|
|
... while True:
|
|
... try:
|
|
... print (yield)
|
|
... except ValueError,v:
|
|
... print "caught ValueError (%s)" % (v),
|
|
>>> import sys
|
|
>>> g = f()
|
|
>>> g.next()
|
|
|
|
>>> g.throw(ValueError) # type only
|
|
caught ValueError ()
|
|
|
|
>>> g.throw(ValueError("xyz")) # value only
|
|
caught ValueError (xyz)
|
|
|
|
>>> g.throw(ValueError, ValueError(1)) # value+matching type
|
|
caught ValueError (1)
|
|
|
|
>>> g.throw(ValueError, TypeError(1)) # mismatched type, rewrapped
|
|
caught ValueError (1)
|
|
|
|
>>> g.throw(ValueError, ValueError(1), None) # explicit None traceback
|
|
caught ValueError (1)
|
|
|
|
>>> g.throw(ValueError(1), "foo") # bad args
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: instance exception may not have a separate value
|
|
|
|
>>> g.throw(ValueError, "foo", 23) # bad args
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: throw() third argument must be a traceback object
|
|
|
|
>>> def throw(g,exc):
|
|
... try:
|
|
... raise exc
|
|
... except:
|
|
... g.throw(*sys.exc_info())
|
|
>>> throw(g,ValueError) # do it with traceback included
|
|
caught ValueError ()
|
|
|
|
>>> g.send(1)
|
|
1
|
|
|
|
>>> throw(g,TypeError) # terminate the generator
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError
|
|
|
|
>>> print g.gi_frame
|
|
None
|
|
|
|
>>> g.send(2)
|
|
Traceback (most recent call last):
|
|
...
|
|
StopIteration
|
|
|
|
>>> g.throw(ValueError,6) # throw on closed generator
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: 6
|
|
|
|
>>> f().throw(ValueError,7) # throw on just-opened generator
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: 7
|
|
|
|
>>> f().throw("abc") # throw on just-opened generator
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: exceptions must be classes, or instances, not str
|
|
|
|
Now let's try closing a generator:
|
|
|
|
>>> def f():
|
|
... try: yield
|
|
... except GeneratorExit:
|
|
... print "exiting"
|
|
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> g.close()
|
|
exiting
|
|
>>> g.close() # should be no-op now
|
|
|
|
>>> f().close() # close on just-opened generator should be fine
|
|
|
|
>>> def f(): yield # an even simpler generator
|
|
>>> f().close() # close before opening
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> g.close() # close normally
|
|
|
|
And finalization:
|
|
|
|
>>> def f():
|
|
... try: yield
|
|
... finally:
|
|
... print "exiting"
|
|
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> del g
|
|
exiting
|
|
|
|
>>> class context(object):
|
|
... def __enter__(self): pass
|
|
... def __exit__(self, *args): print 'exiting'
|
|
>>> def f():
|
|
... with context():
|
|
... yield
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> del g
|
|
exiting
|
|
|
|
|
|
GeneratorExit is not caught by except Exception:
|
|
|
|
>>> def f():
|
|
... try: yield
|
|
... except Exception: print 'except'
|
|
... finally: print 'finally'
|
|
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> del g
|
|
finally
|
|
|
|
|
|
Now let's try some ill-behaved generators:
|
|
|
|
>>> def f():
|
|
... try: yield
|
|
... except GeneratorExit:
|
|
... yield "foo!"
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> g.close()
|
|
Traceback (most recent call last):
|
|
...
|
|
RuntimeError: generator ignored GeneratorExit
|
|
>>> g.close()
|
|
|
|
|
|
Our ill-behaved code should be invoked during GC:
|
|
|
|
>>> import sys, StringIO
|
|
>>> old, sys.stderr = sys.stderr, StringIO.StringIO()
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> del g
|
|
>>> sys.stderr.getvalue().startswith(
|
|
... "Exception RuntimeError: 'generator ignored GeneratorExit' in "
|
|
... )
|
|
True
|
|
>>> sys.stderr = old
|
|
|
|
|
|
And errors thrown during closing should propagate:
|
|
|
|
>>> def f():
|
|
... try: yield
|
|
... except GeneratorExit:
|
|
... raise TypeError("fie!")
|
|
>>> g = f()
|
|
>>> g.next()
|
|
>>> g.close()
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: fie!
|
|
|
|
|
|
Ensure that various yield expression constructs make their
|
|
enclosing function a generator:
|
|
|
|
>>> def f(): x += yield
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f(): x = yield
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f(): lambda x=(yield): 1
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f(): x=(i for i in (yield) if (yield))
|
|
>>> type(f())
|
|
<type 'generator'>
|
|
|
|
>>> def f(d): d[(yield "a")] = d[(yield "b")] = 27
|
|
>>> data = [1,2]
|
|
>>> g = f(data)
|
|
>>> type(g)
|
|
<type 'generator'>
|
|
>>> g.send(None)
|
|
'a'
|
|
>>> data
|
|
[1, 2]
|
|
>>> g.send(0)
|
|
'b'
|
|
>>> data
|
|
[27, 2]
|
|
>>> try: g.send(1)
|
|
... except StopIteration: pass
|
|
>>> data
|
|
[27, 27]
|
|
|
|
"""
|
|
|
|
refleaks_tests = """
|
|
Prior to adding cycle-GC support to itertools.tee, this code would leak
|
|
references. We add it to the standard suite so the routine refleak-tests
|
|
would trigger if it starts being uncleanable again.
|
|
|
|
>>> import itertools
|
|
>>> def leak():
|
|
... class gen:
|
|
... def __iter__(self):
|
|
... return self
|
|
... def next(self):
|
|
... return self.item
|
|
... g = gen()
|
|
... head, tail = itertools.tee(g)
|
|
... g.item = head
|
|
... return head
|
|
>>> it = leak()
|
|
|
|
Make sure to also test the involvement of the tee-internal teedataobject,
|
|
which stores returned items.
|
|
|
|
>>> item = it.next()
|
|
|
|
|
|
|
|
This test leaked at one point due to generator finalization/destruction.
|
|
It was copied from Lib/test/leakers/test_generator_cycle.py before the file
|
|
was removed.
|
|
|
|
>>> def leak():
|
|
... def gen():
|
|
... while True:
|
|
... yield g
|
|
... g = gen()
|
|
|
|
>>> leak()
|
|
|
|
|
|
|
|
This test isn't really generator related, but rather exception-in-cleanup
|
|
related. The coroutine tests (above) just happen to cause an exception in
|
|
the generator's __del__ (tp_del) method. We can also test for this
|
|
explicitly, without generators. We do have to redirect stderr to avoid
|
|
printing warnings and to doublecheck that we actually tested what we wanted
|
|
to test.
|
|
|
|
>>> import sys, StringIO
|
|
>>> old = sys.stderr
|
|
>>> try:
|
|
... sys.stderr = StringIO.StringIO()
|
|
... class Leaker:
|
|
... def __del__(self):
|
|
... raise RuntimeError
|
|
...
|
|
... l = Leaker()
|
|
... del l
|
|
... err = sys.stderr.getvalue().strip()
|
|
... err.startswith(
|
|
... "Exception RuntimeError: RuntimeError() in <"
|
|
... )
|
|
... err.endswith("> ignored")
|
|
... len(err.splitlines())
|
|
... finally:
|
|
... sys.stderr = old
|
|
True
|
|
True
|
|
1
|
|
|
|
|
|
|
|
These refleak tests should perhaps be in a testfile of their own,
|
|
test_generators just happened to be the test that drew these out.
|
|
|
|
"""
|
|
|
|
__test__ = {"tut": tutorial_tests,
|
|
"pep": pep_tests,
|
|
"email": email_tests,
|
|
"fun": fun_tests,
|
|
"syntax": syntax_tests,
|
|
"conjoin": conjoin_tests,
|
|
"weakref": weakref_tests,
|
|
"coroutine": coroutine_tests,
|
|
"refleaks": refleaks_tests,
|
|
}
|
|
|
|
# Magic test name that regrtest.py invokes *after* importing this module.
|
|
# This worms around a bootstrap problem.
|
|
# Note that doctest and regrtest both look in sys.argv for a "-v" argument,
|
|
# so this works as expected in both ways of running regrtest.
|
|
def test_main(verbose=None):
|
|
from test import test_support, test_generators
|
|
test_support.run_doctest(test_generators, verbose)
|
|
|
|
# This part isn't needed for regrtest, but for running the test directly.
|
|
if __name__ == "__main__":
|
|
test_main(1)
|